The 4th Texas had been fully equipped with gun sling in 1862, and images of members of the Texas Brigade show many using US-style gun slings, even on their Enfields (with extra holes punches to accomodate for the difference distance between the sling swivels).  If you need one, here's a great copy of an original by L.D. Haning.

US-type Gun Sling - Sharpsburg